ACTIVITY 1 TO IDENTIFY THE PLANE G H

ACTIVITY 1 : TO IDENTIFY THE PLANE G H E F D A PLANE AT THE TOP : C B PLANE EFGH

G H E F D A C B PLANE ON THE LEFT : PLANE ADHE

G H E F D A PLANE IN THE FRONT : C B PLANE ABFE

G H E F D A PLANE AT THE BACK : C B PLANE DCGH

G H E F D A PLANE AT THE BOTTOM: C B PLANE ABCD

G H E F D A PLANE ON THE RIGHT : C B PLANE BCGF

THE LOCATION OF THE POINT ON TOP OF THE RED DOT TO THE RIGHT OF THE RED DOT IN FRONT OF THE RED DOT AT THE BACK OF THE RED DOT

ON THE TOP OF …. TO THE LEFT OF …. IN FRONT OF …. AT THE BACK OF …. TO THE RIGHT OF …. AT THE BOTTOM OF ….

ACTIVITY 2 : TO DETERMINE THE LOCATION OF A POINT H E G F D A C B POINT TO THE LEFT OF F : POINT E POINT AT THE BOTTOM OF F : POINT B POINT AT THE BACK OF F : POINT G POINT TO THE RIGHT OF D : POINT C POINT ON TOP OF D : POINT H POINT IN FRONT OF D : POINT A

ANGLE BETWEEN A LINE AND A PLANE A LINE PLANE C B

Activity 3 : To Identify The Angle Between Line And Plane H G Normal E F D A The line draw from G and perpendicular to the plane ABCD is call normal C Orthogonal projection B The angle between the line AG and the orthogonal projection, AC is the angle between the line AG and the plane ABCD that is GAC. The line lies on the plane ABCD which joint the point A to the line GC is known as the orthogonal projection of line AG on the plane ABCD.

ACTIVITY 3 : To Identify The Angle Between A Line And A Plane Example 1 a G H E F D A Orthogonal projection G C Normal C B A At the bottom Name the angle between the line AG and the plane ABCD Angle between the line AG and the plane ABCD = GAC.

EXAMPLE 1(b) H E A D Diagram 1(b) G F C B Diagram 1 b shows a cuboid ABCDEFGH. Name the angle between the line HB and the plane ABCD.

ACTIVITY 4 : To find the angle between a line and a plane Example 2(a) H E 12 cm D G 5 cm F 5 cm C 4 cm A Diagram 2 a B Diagram 2(a) shows a cuboid, ABCDEFG. Find the angle between the line AH and the plane DCGH.

No Steps Solutions 1. Draw the line AH and shade the plan DCGH in diagram 2 a. H 12 cm G 5 cm E F D A Diagram 2 a C 4 cm B Diagram 2 a shows a cuboid, ABCDEFG. Find the angle between the line AH and the plane DCGH.

No Steeps Solutions 2 Use the method you have learned in activity 3, identify the angle between the line AH and the plane DCGH A back H E D 12 cm G F 5 cm C 4 cm A B H D

No Steps 3 Refer to the points you have obtained in steep 2 (point A, H, D), complete the ∆ AHD. Mark the right angle, HDA. Transfer out the ∆ AHD. A H Solutions H D E H A D 12 cm 5 cm D G F 4 cm A B C

No Steps 4 With the information given in the Solutions question, label the length of the sides of ∆ AHD. At least the length for 2 sides must be known. Use Pythegoras Theorem if necessary. H 5 cm A 4 cm H E A D 12 cm G F B 5 cm C 4 cm D

No Steps Solutions 6 Mark, - the opposite side, AD as. T - the adjacent side, HD as S H 5 cm A 4 cm T H E D 12 cm G F 5 cm C 4 cm A B D S

No Steps Solutions 6 Use the tangent formula to calculate AHD. Remember, use -The sine formula, if O and H were known - SOH Tan AHD = tan -1 AHD = 38040’ - The cosine formula, if A and H were known – CAH -The tangent formula, if O and A were known – TOA H E D 12 cm F G 5 cm C 4 cm A B

example 2 (b) H 12 cm E G F D 4 cm C 3 cm A Diagram 2 b B Diagram 2 b shows a cuboid, ABCDEFGH. Calculate the angle between the line HB and the plane BCGF

ANGLE BETWEEN TWO PLANES

ACTIVITY 5 : To Identified The Angle Between Two Planes EXAMPLE 3(a) G H E D F C 1. DRAW 3 LINES A B Diagram 3 a shows a cuboid, ABCDEFGH. Name the angle between the plane AGH and the plane ABCD

ACTIVITY 5 : To Identified The Angle Between Two Planes G H E D F C Bottom A B Diagram 3 a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD 2. Mark the location (direction) of the plane ABCD at the bottom of the first line to the left.

ACTIVITY 5 : To Identified The Angle Between Two Planes G H A E D A F C B Diagram 3 a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD Bottom 3. Refer to the plane, AGH, identify the points which touch the plane, ABCD and write it at the middle line.

ACTIVITY 5 : To Identified The Angle Between Two Planes G H H/G E D A A F C B Diagram 3 a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD Bottom 3. Refer to the plane, AGH, identify the point which does not touch the plane, ABCD and write it at the first line to the left.

ACTIVITY 5 : To Identified The Angle Between Two Planes G H E D A H/G A Bottom F C B Diagram 3 a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD 5. Between the point H and G, point which is nearer to point A or located on the same plane as point A will be choosen. Point which is not choosen will be earased.

ACTIVITY 5 : To Identified The Angle Between Two Planes G H E D A H A Ke Bawah F C B Diagram 3 a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD 5. Between the point H and G, point which is nearer to point A or located on the same plane as point A will be choosen. Point which is not choosen will be earased.

ACTIVITY 5 : To Identified The Angle Between Two Planes G H E D A C Diagram 3 a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD A D Bottom F B H 6. Identify the point which is located at the bottom of the point H ( )and write it on the first line to the right.

ACTIVITY 5 : To Identified The Angle Between Two Planes G H H E D A D F C B Diagram 3 a A Bottom 7. In the diagram 3 a, complete the ∆ HAD and mark the HAD Angle between the plane, AGH and the plane, ABCD = HAD

EXAMPLE 3(b) H 12 cm E D A Diagram 3 b F G 5 cm C 4 cm B Diagram 3 b shows a cuboid with horizontal rectangle base ABCD. Name the angle between the plane ACH and the plane CDHG

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